A sampling rate converter is used to change a sampling frequency of a digital signal, and may also be referred to as a re-sampler. A sampling rate converter may take the form of a hardware device and/or software, and may be either an up-sampler or a down-sampler. An up-sampler increases the sampling rate of a digital signal. A down-sampler reduces the sampling rate of the digital signal. A sampling frequency conversion rate is defined to be the ratio of a desired output sampling frequency to a given input sampling frequency. An up-sampling conversion rate is always greater than 1.0, while a down-sampling conversion rate is always less than 1.0.
Aliasing is a phenomenon that usually occurs when converting an analog signal to a digital signal, or vice versa. Aliasing may also occur when converting the sampling frequency of a digital signal. When aliasing occurs, signal energy at one frequency is imaged to other frequencies. For example, suppose a signal has two sinusoidal components at 1 kHz and 7.5 kHz, respectively. If the signal is sampled at 16 kHz, the signal can be reconstructed perfectly. If the signal is down-sampled to 4 kHz from 16 kHz by decimation, the energy at 1 kHz will not change, but the energy at 7.5 kHz will be imaged to 0.5 kHz. The energy at 0.5 kHz is considered aliasing. As another example, if an analog sinusoidal signal at 1 kHz is sampled at 4 kHz, the energy will appear to be at 1 kHz, which is desirable. However, if the signal is up-sampled to 16 kHz by inserting three zeros between adjacent samples, the energy will appear to be at 1 kHz, 3 kHz, 5 kHz and 7 kHz. The energy at 3 kHz, 5 kHz and 7 kHz is an image of the energy at 1 kHz and is considered aliasing. To reduce distortion due to aliasing, sampling rate converters typically include an anti-aliasing filter, which is generally a low pass filter.
Anti-aliasing filters are generally needed in both up-samplers and down-samplers. For example, a conventional down-sampler typically includes an anti-aliasing filter and a decimator. In some cases, a down-sampler may include a digital-to-analog converter that converts an original digital signal to an analog signal, and an analog-to-digital converter that samples the analog signal at a desired sampling frequency. However, this type of down-sampler requires dedicated hardware support, which can increase the size and cost of the down-sampler.
In other cases, a down-sampler may perform sampling frequency conversions strictly in the digital domain. A digital domain down-sampler can be implemented in three stages when the down-sampling rate is expressed as a ratio of two positive integers. As an example, let the down-sampling rate be I/D, where I and D are relatively prime positive integers and D is strictly greater than I. First, the digital signal is interpolated by a factor of I. Then, an anti-aliasing filter filters the interpolated digital signal. Last, the digital signal is decimated by a down-sampling factor of D. The bandwidth of the anti-aliasing filter in the down-sampler is π/D, where D is the down-sampling factor. Therefore, each different down-sampling rate D requires a different anti-aliasing filter. A single prototype anti-aliasing filter may be used to generate an anti-aliasing filter for each desired sampling rate using linear interpolation. However, in order to achieve high performance, a very narrow band prototype anti-aliasing filter with a large number of coefficients is required.